Get Active disturbance rejection control for nonlinear systems : PDF

By Bao-Zhu Guo, Zhi-Liang Zhao

ISBN-10: 1119239931

ISBN-13: 9781119239932

ISBN-10: 111923994X

ISBN-13: 9781119239949

ISBN-10: 1119239958

ISBN-13: 9781119239956

A concise, in-depth advent to energetic disturbance rejection regulate concept for nonlinear platforms, with numerical simulations and obviously labored out equations

  • Provides the elemental, theoretical beginning for functions of lively disturbance rejection control
  • Features numerical simulations and obviously labored out equations
  • Highlights some great benefits of energetic disturbance rejection keep watch over, together with small overshooting, speedy convergence, and effort savings

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Extra info for Active disturbance rejection control for nonlinear systems : an introduction

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49), we can obtain that V (x(t; x0 )) is nonincreasing as t increases. This together with the positive definiteness and continuity of V (x) gives lim V (x(t; x0 )) = V (x∗ ) > 0. 45) starting from x∗ . 49), we have V (x(t; x∗ )) < V (x∗ ) for all t > 0. 52) which implies that {x(t; x∗ )| t ≥ 0} ⊂ Lf V −1 (0). This is a contradiction. Hence there exists t1 > 0 such that V (x(t1 ; x∗ )) < V (x∗ ). 4 that there exists a sequence {t∗n } such that lim x(t∗n ; x0 ) = x(t1 ; x∗ ), n→∞ which yields lim V (x(t∗n ; x0 )) = V (x(t1 ; x∗ )) < V (x∗ ).

111) Proof. In what follows, we need to take frequently a convergent subsequence from a sequence of numbers or functions. For the sake of simplicity, we avoid using multiple indices and just assume that the given sequence itself is convergent. According to the second item of the conditions on F (t, x), there exists M > 0 such that for any t ∈ [−1, R + 1] \ N0 and x ∞ ≤ R + 1, F (t, x) ⊂ BM (0). For any j ≥ 0 and t ∈ [−1, R], set ⎧ ⎪ x (t1 ), if − 1 ≤ t ≤ t1j , ⎪ ⎨ j j x ˜j (t) = xj (t), if t1j ≤ t ≤ t2j , ⎪ ⎪ ⎩ xj (t2j ), if t2j ≤ t ≤ R.

This together with the positive definiteness and continuity of V (x) gives lim V (x(t; x0 )) = V (x∗ ) > 0. 45) starting from x∗ . 49), we have V (x(t; x∗ )) < V (x∗ ) for all t > 0. 52) which implies that {x(t; x∗ )| t ≥ 0} ⊂ Lf V −1 (0). This is a contradiction. Hence there exists t1 > 0 such that V (x(t1 ; x∗ )) < V (x∗ ). 4 that there exists a sequence {t∗n } such that lim x(t∗n ; x0 ) = x(t1 ; x∗ ), n→∞ which yields lim V (x(t∗n ; x0 )) = V (x(t1 ; x∗ )) < V (x∗ ). 50). The result is thus concluded.

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Active disturbance rejection control for nonlinear systems : an introduction by Bao-Zhu Guo, Zhi-Liang Zhao


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